Question

Give the newtons formula for the velocity of sound in air and state its assumptions

Answer 1

According to gas law (Boyle's law),

PV = constant

where, P = pressure

V = volume of air

Differentiating above equation, we get

Differentiation of Boyle's Law

where, B is the bulk modulus of the air.

If B is the bulk modulus of the air, v is velocity and ρ is the density, then, velocity is given by:

Relationship of velocity or air with bulk modulus and density

This is the required expression for velocity of sound in air.